The Frenet-Serret formulae relate torsion and this quantity to a set of three vectors. One type of this quantity is given as the determinant of the sh
The Frenet-Serret formulae relate torsion and this quantity to a set of three vectors. One type of this quantity is given as the determinant of the shape operator and is the product of the two "principal" values of this. The "intrinsic" type of it is undetectable to observers who are not on the manifold, and is exemplified by the Gaussian type of this quantity, while the Ricci and Reimann tensors also describe this property. The "extrinsic" type is defined as the derivative of the tangent angle with respect to the arclength at a point.  This quantity is the inverse of the radius of the osculating circle associated with a curve. For 10 points, identify this quantity which roughly describes how much a plane or a line is bent. 
The Frenet-Serret formulae relate torsion and this quantity to a set of three vectors.
{curvature} [accept {torsion} until mentioned]